提出语义信息G理论，实现目标性与效率的平衡控制。
Semantic Information G Theory for Range Control with Tradeoff between Purposiveness and Efficiency
- 引入语义信息G度量与率保真函数R(G)，建立信息效率优化框架。
- 参数解可调控范围控制中目标性与效率的权衡，提升系统性能。
- 适用于深度学习、强化学习中的信息优化问题，具有理论潜力。
深度学习的最新进展表明，需同时最大化和最小化两类信息。信息最大-最小（IMM）方法已应用于深度学习、强化学习及最大熵控制。香农的信息率-失真函数是最小互信息（MMI）与数据压缩的理论基础，但不足以解决IMM问题。作者提出了语义信息G理论（即香农-陆理论），包括语义信息G度量和信息率保真函数R(G)（R为给定语义互信息G下的MMI）。R(G)函数的参数解提供了一种通用方法，以提升信息效率G/R。本文简要介绍语义信息G度量及R(G)函数的参数解。两个实例表明，该参数解有助于优化范围控制中目标性（即语义互信息）与信息效率的权衡。尽管R(G)函数可能成为IMM方法的理论基础，仍需结合深度学习、强化学习与约束控制进一步研究。
原文摘要 · Abstract (English)
Recent advances in deep learning suggest that we need to maximize and minimize two different kinds of information simultaneously. The Information Max-Min (IMM) method has been used in deep learning, reinforcement learning, and maximum entropy control. Shannon's information rate-distortion function is the theoretical basis of Minimizing Mutual Information (MMI) and data compression, but it is not enough to solve the IMM problem. The author has proposed the semantic information G theory (i.e., Shannon-Lu theory), including the semantic information G measure and the information rate fidelity function R(G) (R is the MMI for the given G of semantic mutual information). The parameter solution of the R(G) function provides a general method to improve the information efficiency, G/R. This paper briefly introduces the semantic information G measure and the parametric solution of the R(G) function. Two examples reveal that the parametric solution can help us optimize range control with the tradeoff between purposiveness (i.e., semantic mutual information) and information efficiency. It seems that the R(G) function can serve as the theoretical basis of IMM methods, but we still need further research in combination with deep learning, reinforcement learning, and constraint control.
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